Exact results of the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

By Han-dong Chen, Zohar Nussinov. 2007

175 citations recorded by the source corpus.

In this work, we illustrate how a Jordan–Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan–Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves and (v) express the local symmetries of Kitaev's model and the anyonic character of the excitations in terms of fermions.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/dbd24272ff2298ed639a6aa8b2b25ab82762ed4d

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In Atomic and Molecular Physics, and Optics

1. Yi Zhou
2. T. Ng
3. K. Kanoda

In Condensed Matter Physics

1. Yi Zhou
2. T. Ng
3. K. Kanoda

Citations in the corpus

• Quantum spin liquid states (2016, methodology): “The spin wavefunction can be obtained from the fermion model, and the anyonic character of the vortex excitations in the gapped phase also has an explicit fermionic construction (Chen and Nussinov, 2008).”